Introduction to Inferential Statistics

Question 1

How can we infer something about the population based on what we find in the sample?

Answer 1

Normal distribution
Empirical rule
Central limit theorem

Question 2

Are t-values and standard errors used to estimate population parameters?

Answer 2

Yes

Question 3

What are inferential statistics used for?

Answer 3

To draw conclusions and make inferences about population parameters by analyzing data collected in a sample
To infer something about the population parameter using sample statistics

Question 4

Will parameter estimates based on a sample exactly equal the population parameter?

Answer 4

No, because they vary from sample-to-sample
So, when reporting a statistic, we also typically report an interval (e.g., 95% confidence interval) which we believe includes the population parameter

Question 5

What is a confidence interval?

Answer 5

A range of values within which a population parameter (e.g., mean or proportion) is likely to fall, based on a sample from that population
If you repeated a study of the same size many times, 95% of the resulting confidence intervals would cover (include) the true population parameter

Question 6

Do statistics estimate the sample?

Answer 6

Yes
And parameters estimate the population

Question 7

Since samples describe the population, do statistics describe the parameters?

Answer 7

Yes

Question 8

What notations are used for samples?

Answer 8

Number of people: n
Mean: X (with a bar on top)
Variance: s^2
Standard deviation: S or SD

Question 9

What notations are used for the population?

Answer 9

Number of people: N
Mean: mu
Variance: sigma^2
Standard deviation: sigma

Question 10

What are the primary characteristics of a normal distribution?

Answer 10

Symmetric and unimodal (one peak)

Question 11

Why is a normal distribution the most important distribution in inferential statistics?

Answer 11

It’s characteristics form the foundational assumptions underlying many interferential statistics

Question 12

Can you apply the empirical rule to any normal distribution?

Answer 12

Yes

Question 13

What is the empirical rule?

Answer 13

68% of the observations fall within 1 standard deviation of the mean
95.4% of the observations fall within 2 standard deviations of the mean
99.7% of the observations fall within 3 standard deviations of the mean

Question 14

If something has a normal distribution, can you use the central limit theorem?

Answer 14

Yes

Question 15

What are the three distributions?

Answer 15

Sample distributions (distribution of the sample)
Population distribution (distribution of the population)
Sampling distribution (distribution of a statistic over a set of of theoretical samples; distribution of sample means; plotted means of various samples)

Question 16

Is the sampling distribution of the sample means approximately normal?

Answer 16

Yes
The sampling distribution of the sample means becomes “more normal” as n (or number of samples) increases
The mean of the sampling distribution of sample means will be the same as the mean of the population

Question 17

Since the distribution of the sample means is approximately a normal distribution, can the empirical rule be applied?

Answer 17

Yes

Question 18

Do we know that 95% of all sample means are within 2 SDs of the population mean?

Answer 18

Yes, based on the empirical rule
This theoretical assumption is the basis for inferential statistics

Question 19

What is the standard error of the mean?

Answer 19

Analogous to the SD of the population data
SEM = SD of the sample/square root of the sample size

Question 20

How is the standard deviation related to the sample error of the mean?

Answer 20

Just as the standard deviation increments the distance of a raw score from the population mean, the SEM increments the distance of the sample mean from the population mean

Question 21

What will make the SEM change?

Answer 21

The SD of the sample
The size of the sample

Question 22

Why are the standard error (SD) increments of the distribution of the sample means so much narrower?

Answer 22

Because we are just plotting means, not raw scores
Outliers are not applied

Question 23

What are z-scores?

Answer 23

Indicate how far a score is from the mean in a population context
Raw scores incremented by standard deviation units
A z-score indicates how far a raw score is from the population mean

Question 24

What are t-scores?

Answer 24

Indicate how far a score is from the mean in a sample context
Sample means incremented by standard error units
A t-score indicates how far a sample mean is from another mean
Sample means are distributed following the t-distribution

Question 25

Do t-scores differ depending on sample size?

Answer 25

Yes

Question 26

Is there a different t-distribution for each discrete number of degrees of freedom?

Answer 26

Yes aka sample sizes

Question 27

As the sample size increases, does the t-value get closer to the z-score?

Answer 27

Yes

Question 28

What is a confidence interval?

Answer 28

The interval (range of scores) which we believe includes the population parameter We can be 95% confident that ______ on average between...

Question 29

Since we rarely know the population mean, what do we use instead?

Answer 29

the mean score of our sample the standard error of the mean the assumption that the sampling means are normally distributed (so we can apply the Central Limit Theorem)

Question 30

What is a critical t value?

Answer 30

The “critical value” is the cutoff point for 5% of the distribution A test statistic value (t) exceeding the cut-off point is statistically significant, p<0.05

Question 31

What do narrower confidence intervals indicate?

Answer 31

The more precisely we have estimated the population parameter Generally, the width of the confidence interval is inversely related to the size of the sample

Question 32

What are the four sources of variability?

Answer 32

Differences attributable to group membership (between group) Sampling error (within group) Measurement error (within group) Individual differences (within group)

Question 33

What is important to determine when comparing groups?

Answer 33

Does one group constitute their own population If 95% CI do not overlap between groups, the difference is significant (p<0.05)

Question 34

If the 95% CI do overlap, is the difference significant?

Answer 34

No, p>0.05

Question 35

How do you calculate the critical t score when you are comparing groups?

Answer 35

Based on the total number of subjects minus 2 *used when calculating the 95% CI around the mean difference for two groups

Question 36

What are the two approaches for comparing the 95% CI of two groups?

Answer 36

Do CI for each group separately and then see if they overlap 95% CI around the mean difference (CI for the difference in mean between groups; if the interval crosses zero, they are not significantly different)